Mathematics in Empire - how much can we assume?

The very specific question I am wondering about is “can we assume our characters know about basic probability”.

The broader question is “how much maths should we assume is known in the setting”?

The wiki page on Technology has a little bit about literacy and numeracy, but there’s only one paragraph about maths:

In terms of mathematics, the Empire is quite advanced compared to the medieval world. Algebra and geometry are well understood, and some scholars (especially in Urizen) explore the world of numbers with a similar fervour to that with which wizards study the realm of magic.

I’d take that as implying that most of the stuff you learn in maths GCSE is okay (and after all, a fair number of adult players are going to have done maths GCSE and might remember that stuff).

Thing is, basic probability is also part of maths GCSE… but probability theory itself as developed by Pascal started in the 17th century, so “compared to the medieval world” doesn’t help so much there.

Is this something I should check with PD?

Probably best to ask for specific questions, but I believe previous rulings were that Urizen, and the empire at large, were very good at Maths, aided by Day Eternals, Ylenrith especially, to the point where pretty much any maths or logic was good.

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I’d advise a lot of pure maths is very good for Urizen.
Probability was only formalised in the 17th century, in the medieval era there was a lot of gambling going on, and so you get a kind of intuitively based probability theory (which a league character could well be very good at), which is suprisingly close to GCSE level

Ofc military council is just maths club, like I got in a convo IC with a guy who goes to it talking about what I though a good strategy would have been (cos im a history strategy nerd) and he just started rattling off numbers and stats for the manovers and battles

Military council uses, essentially, arithmetic. That’s not relevant to this discussion.

This is a really good question. I don’t think Ricohard is correct - I’m not sure calculus exists, for instance. The modernness of probability often surprises people too as you say. I think a good rule of thumb is “late 1500s-ish”.

It’s worth remembering that the modern properly rigorous abstract mathematics approach is about as old/younger than than the telephone, the camera, X-rays, aeroplanes. So while we /might/ touch on it with Ylenrith… it’s quite outside scope and themes.

It would be fascinating to work out the history of mathematics within the setting, I think. I wonder where zero came from.

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Finding the origin (ha!) of zero sound like an EXCELLENT use of a historical research request, and not trivial or frivolous at all! Someone should totally do that, it would be amazing


I know that there’s a bunch of Information theory and mathematics, as an example, that were historically fairly recent discoveries in our world but would have been fairly obvious given Urizeni work with the Heliopticon. I can’t remember the specifics but I do remember then Archmage Iulian giving a talk on them at a Player event.

Yeah, that’s adding to my impression that the answer is a difficult one.

To add to my original question: while one of the things I wanted to know this for was whether it was sensible to think you could calculate “how likely is X to happen again when we do Y, given that a variety of people have done Y N times in the last 5 years and X has happened M times” to some degree of usefulness, the other reason I was wondering about it was for doing statistical analysis of language. Specifically corpus linguistics.

Then I remembered that the terminology for parts of speech I was thinking of was developed in, uh, mainly the 1960s.

Then I read up on the history of linguistics and particularly modern linguistics and remembered that that stuff is even newer than I thought (1800s before you’re getting something looking vaguely modern, and a lot of stuff I learned at university is 1900s onwards).

So that’s an even thornier question!

Speaking as someone with the capability to submit historical research it is not a request I would expect to get useful information from.

IC reasoning: Because historical researchers need a starting point, so at minimum I would want a name, a date, and a place for research.

OC reasoning: Because it is better for PD if they can link the output of research requests into existing plot, a certain amount of consideration for their content is helpful for the crew who have to write them. And because I would prefer to submit a request that more people than the highly mathematically inclined would be able to both write, and understand when it was written.


“Something that a player did at a player event” does not a wide precedent set.


Yup, that sounds like a modern player who’d studied maths to a reasonably high level (he’s a physicist) explaining something cool that you could explain with IC-appropriate concepts, but doesn’t necessarily tell you what’s going to be common around the entire world. :slight_smile:

The problem with science and stuff in Empire, compared to the real world, is that the real world’s fabric doesn’t decide to change whenever the Wanderer decides things are stale.


I don’t know my way round the maths too well but from a sociological perspective, I would expect probability to develop if anything late in the Empire world. IC Conjunctions seem to be not predictable in advance (because oc they are skins for PD rules changes and so on, what sort of rules will need changing oc is not IC predictable) and change the nature of reality on a basis of roughly four times a year. Add this to Highborn attitudes to history and I think you get a universe where believing the same thing happens with perfect predictable regularity is not philosophically obvious…

I’m not sure I agree.

The less predictable something is the more complex the tools to do so need to be, certainly the civil service can and do ‘predict’ some of these effects. But the mechanisms to do are below the abstraction layer and not physep-able with real maths. But that doesn’t mean the maths doesn’t exist.

Also with the emphasis though in the way on “evidence base” there is a much larger theological argument to develop significance testing.
In the real world (AIUI) a lot of philosophy came from religious ‘needs’. I could easily see that in the empire that could develop into an understanding of probability and desire to research significance testing.

Another point is we’ve had enciphered documents to break from the plot team whose cipher wasn’t broken until the Victorian age - so the

Finally I’ve heard much more recent theorems IC discussions from other players; including Gödels incompleteness theorem. Although you could argue this is players playing outside the setting a little bit to much.

Not sure where that gets us though.

Considering that Highborn, too, prefer games of skill to games of pure chance means that basic knowledge of the difference between random luck and actual odds/skill-modified-probability exists in the general populace. How likely it is to be more in-depth than the odds of certain cards appearing in a game of poker, for example, I couldn’t say with any confidence.

This has come up before (maybe a couple of times), but I can’t find the thread anywhere. There were actual mathematicians on that thread, as well as people who like me with an interest and can fake ability in the field. I know that Iulian’s player was one of them and he’ll probably turn up soon

I know that someone (Iulian?) attempted to use an Arcane Projection to discover whether the World obeyed the Axiom of Choice, that was Denied with Menaces

If memory serves then we decided that if we took out formal proof by induction and anything that requires it then that left plenty of interesting stuff for those of us who wanted to play with it, without getting too modern. No calculus of limits, for example. Information theory has come up at a player event - as has been said

I think that Raff popped up on the original thread to say (and I’m summarising) if you don’t break immersion or try using to prove that Orbital Mind-Control Lasers should totally be a thing, you’re golden

So probability theory is fine - sure it took until the 17th century in this world for formal work to be done, but it could have happened any time there was a decent university in a city that also liked gambling. My headcanon is that it came out of the School of Epistemology

As for your specific question about statistical analysis of language, you can’t do decryption without it and there’s been at least one plot-related cypher that was cracked by letter distribution methods. So I’d say go for it


Gah - I have a maths degree, and following that link down the wikihole of advanced theoretical mathematics still hurt my brain. I simultaneously miss learning about stuff like that and do not miss at all the knots it requires tying your brain into.

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I had a look around on the forum archives, and the initial post for the Processes of Reason event has what I reckon was a good rule of thumb to pitch ideas at:

The format would be a series of short talks from volunteer speakers on entertaining, new* or favourite topics in the fields of natural philosophy, moral philosophy, theology, mathematics, logic or basically anything that people in metaphorical or actual pointy hats might study

with the * pointing to this footnote:

Not actually new! If someone proves Riemann in February 2015, please don’t bring a copy of their proof to the event IC! On an out-of-character note, apart from a potential ‘freestyle’ session, the topics presented will be at a level aimed at the bright and interested sixth former / non-expert (think Goedel, Escher, Bach or the early parts of the Feynman lectures); the idea is to entertain, and to give us something to sit around and feel like Proper Academic Wizards discussing, not to cause Day curse RP effects out of character or to line up our groups’ respective maths academics and make them fight (unless, y’know, they want to engage in chessboxing). Acceptable topics are basically anything without icky computer science cooties on, but please be sensible about this - there are vast swathes of mathematics that would make sense without us having to get our lovely high fantasy setting all icky with modern thought.

This was written from a then-player’s perspective but works pretty well with what I was thinking as an aim - assume Maths GCSE for most people, aim at interested sixth-former level if you’re going for something more erudite. :slight_smile:

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So I would encourage people with maths interest to go sideways rather than upwards - geometry, not calculus. You can calculate compound interest geometrically. Probability as a whole didn’t exist in the middle ages and likely doesn’t exist in its modern form IC. The scientific method doesn’t work on long timebases in the Empire setting - inferential logic itself isn’t quite valid because of conjunctions, and the mere process of using mathematical methods to approach a problem may perturb it.

Any answer you did get to questions about this would not be coming from a position of lack of expertise, though - of that I can assure you.

Leviathan, for example, isn’t running a statistical model of the world for those Asimov-be-plagiarised psychohistorical observations - Leviathan IS WATCHING and IS AN EXPERT.

But if you wish to call upon f/ex Ylenrith using goetia, I strongly suggest mathematics as a decent way to do it.

I guess the question is - what are you trying to do with the maths?

See also the following quote, which I love for all fantasy settings everywhere:

Neo: “Doesn’t harvesting human body heat for energy violate the laws of thermodynamics?”

Morpheus: “Where’d you learn about thermodynamics, Neo?”

Neo: “In school.”

Morpheus: “Where’d you go to school, Neo?”

Neo: “Oh.”

Morpheus: “The machines tell elegant lies.”


Hi, I played Ylenrith!
If I remember rightly, the ruling was that the empire’s mathematics is as good as our modern understandings of mathematics. The difference is that your average pleb in Empire is probably much less educated on maths than the average pleb IRL. However, those who study have the same degree of knowledge.
In play, ‘do you know maths’ is treated much like ‘do you know Sarcovan/dutch’. It’s a hard-skill that you might have.
It’s worth noting that Ylenrith’s interest is much more with the ‘pure mathematics’ side of things. She likes, for example, elegant proofs. Set theory and formal logic fit her area of interest; statistics is less her thing.
Certainly, some of the challenges Ylenrith (and her heralds) have sent out at events have been quite difficult maths. In character, I’ve had some very interesting discussions with PCs (who’s players were legit mathematicians, I think) on the matter.

I suspect that this is because a lot of Empire’s players are good at maths and enjoy solving difficult puzzles, and so if there’s a limit on what maths ‘exists’ in the world, there’s a similar limit on what puzzles can be sent out to challenge these players. I have genuinely seen players sat with a big page of weird calculus (if I remember right) problems to solve, and having fun working on it.

Science doesn’t work like it does in the real world, but maths does.